Experimental (vapour + liquid) equilibrium data and modelling for binary mixtures of decafluorobutane with propane and 1-butene

J. Chem. Thermodynamics 67 (2013) 134–142

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Experimental (vapour + liquid) equilibrium data and modelling for binary mixtures of decafluorobutane with propane and 1-butene Shalendra Clinton Subramoney a, Paramespri Naidoo a, Alain Valtz b, Christophe Coquelet a,b, Dominique Richon a, Deresh Ramjugernath a,⇑ a b

Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, South Africa MINES ParisTech, CTP – Centre Thermodynamique des Procédés, 35 Rue Saint Honoré, 77305 Fontainebleau, France

a r t i c l e

i n f o

Article history: Received 20 May 2013 Received in revised form 24 July 2013 Accepted 25 July 2013 Available online 2 August 2013 Keywords: Phase equilibria (Vapour + liquid) equilibria VLE ‘‘Static analytic’’ method Decafluorobutane 1-Butene Propane Modelling

a b s t r a c t (Vapour + liquid) equilibrium (P–x–y) data are reported at three isotherms for the (propane + decafluorobutane), and (1-butene + decafluorobutane) binary systems. The range of temperatures extended from 312.92 K to 342.94 K. An apparatus based on the ‘‘static-analytic’’ method, which had two electromagnetic ROLSITM samplers, for repeatable and reliable equilibrium phase sampling and handling, was used to undertake the measurements. The experimental values were correlated with the ‘‘PR–MC–NRTL–WS’’ model which comprised the Mathias–Copeman alpha function, Wong–Sandler mixing rule, and NRTL local composition model which were incorporated into the Peng–Robinson equation of state. Maximum pressure azeotropy is observed for both systems at all investigated temperatures. Liquid–liquid immiscibility was not observed over the range of temperatures studied. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction This study forms part of a large research programme, currently being undertaken in the Thermodynamics Research Unit at the University of KwaZulu-Natal, on the thermodynamic properties of fluorocarbons and their mixtures. One of the main objectives of the programme is the development of an extensive experimental property database which would enable the investigation of novel fluorocarbon technologies. Some of the previous studies undertaken have reported pure component saturated vapour pressures and densities for a perfluoroolefin and a perfluoroepoxide [1,2], and (vapour + liquid) equilibria for binary mixtures involving perfluoroalkanes or perfluoroolefins [3–6]. The current study involves (vapour + liquid) equilibrium measurements for (perfluorocarbon + hydrocarbon) systems, with this manuscript presenting equilibrium data for binary mixtures involving a hydrocarbon and a perfluoroalkane, viz. (propane + decafluorobutane), and (1-butene + decafluorobutane). The anomalous behaviour of fluorocarbon solutions has attracted significant research interest [7–14]. Perfluoroalkane and hydrocarbon mixtures are known to exhibit atypical behaviour

⇑ Corresponding author. Tel.: +27 31 2603128; fax: +27 31 2601118. E-mail address: [email protected] (D. Ramjugernath). 0021-9614/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jct.2013.07.020

for mixtures of non-polar fluids with substantial deviations from ideality and extensive regions of liquid–liquid immiscibility [7,8,15]. Such counter-intuitive behaviour has led to numerous and varied applications of fluorocarbon solutions, such as surfactants, elastomers, polymers, water resistant textiles, pesticides, pharmaceuticals, and blood substitutes [14]. In the context of refrigerants, low molar mass fluorocarbons such as R-14 are used for low temperature cascade systems [16], or as constituents in specialty refrigerant mixtures such as R-507 (R-152a/R-218) [17], R-508 (R-23/R-116) [18], and R-509 (R-22/R-218) [19]. Perfluorocarbons are also well known for their high ability to dissolve gases [14]. In this context, fluorocarbons can be investigated as potential enhancing agents in separation processes, in particular for the absorption of common petroleum refinery gases [3]. A convenient tool for the development of chemical and separation technologies is process simulation. Central to most simulations is the calculation of thermodynamic properties at each process condition via a thermodynamic model [20]. Cubic equations of state (EoS) are most commonly used for the design of equilibrium stage separation processes as they provide a good balance between accuracy and simplicity [21]. For any thermodynamic model, the most reliable property estimates are achieved through the fitting of model parameters from reliable experimental ‘‘training’’ data, usually measured at representative process conditions. Considering decafluorobutane, a saturated perfluoroalkane,

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bibliographic studies indicate a scarcity of phase equilibrium measurements in the open literature. The data of Simons and Mausteller [22] for the (n-butane + decafluorobutane) binary system remains the only reported VLE data outside of the measurements previously reported in this research program [3,4]. In the present work, novel VLE data for the binary systems (propane + decafluorobutane), and (1-butene + decafluorobutane) are reported over the 312.92 K to 342.94 K temperature range. Saturated vapour pressures for decafluorobutane and propane are also reported over the temperature range of the VLE measurements. The measurements have been conducted on an apparatus based on the ‘‘static-analytic’’ method taking advantage of two electromagnetic ROLSITM capillary samplers [23] for reliable equilibrium phase sampling and handling. The experimental data are represented using the ‘‘PR–MC–WS–NRTL’’ model composed of the Mathias–Copeman alpha function [24], Wong–Sandler mixing rule [25], and non-random two-liquid (NRTL) local composition model [26] associated to the cubic Peng–Robinson EoS [27]. 2. Experimental 2.1. Materials Decafluorobutane (C4F10, CAS number: 355-25-9) was supplied by Pelchem (South Africa), with a certified purity higher than 0.995 volume fraction. Propane (C3H8, CAS number: 74-98-6) was supplied by Messer–Griesheim (France), with a certified purity higher than 0.9995 volume fraction. The 1-butene (C4H8, CAS number: 106-98-9) was supplied by Aldrich (Germany), with a certified purity higher than 0.99 volume fraction. Gas chromatographic analysis of each chemical did not reveal any significant impurities and the chemicals were used as is. The provenance and purity are listed in table 1a.

transducer (0 to 6) MPa that is always connected, and a low pressure transducer (0 to 0.6) MPa that can be bypassed by an isolation valve. Only the high pressure transducer (PT) is used in the present work. The pressure transducer was maintained at a constant temperature above the highest temperature of the measurements through a PID regulator (TR) (WEST, USA, Model 6100) connected to a heating resistance. The signals from the temperature and pressure sensors are transmitted to a data acquisition unit (Agilent, USA, HP34970A) connected to a personal computer system (PC) for real time data logging. Two Monel capillary tubes extend into the equilibrium cell from the top stainlesssteel flange, and are positioned to allow independent sampling of the vapour and liquid phases. The capillaries are connected to two electromagnetic ROLSITM samplers (LS and VS) supplied by ARMINES-Transvalor. ROLSITM is a trademark of ARMINES, it is protected by several patents (PCT patent 2004/090508, PCT patent 2000/011462, EPO patent EP 1105722). A helium carrier gas line is connected to each ROLSITM sampler for carrying the equilibrium samples to a gas chromatograph (GC) (Perichrom, France, PR-2100) for analysis. The GC unit is equipped with a thermal conductivity detector (TCD) and fitted with a packed column (Restek, France, 5% Krytox on CarboBlack B, Stainless steel, 60/80 mesh). All transfer lines are heated and insulated to ensure that the analyzed samples are representative of the equilibrium cell contents (no condensation and no adsorption in the walls of the transfer lines). The electromagnetic ROLSITM samplers are actuated using a dedicated control box (SC) that allows control of the ROLSITM sampler opening time with a 0.01 s resolution. For a given equilibrium cell pressure, the mass of sample withdrawn by the ROLSITM samplers can be adjusted through varying the specified opening time. GC peak area analyses and integrations are performed with the data acquisition software WINILAB III (Perichrom, France, Ver. 4.6).

2.3. Calibrations 2.2. Apparatus A flow diagram of the experimental apparatus is shown in figure 1. The ‘‘static-analytic’’ VLE still used in this work is similar in concept to that of Laugier and Richon [28] and identical to Valtz et al. [29], so only a brief description is given here. In ‘‘static-analytic’’ methods, equilibrium of an enclosed mixture is attained via rapid agitation, usually through efficient stirring. Vapour and liquid phases are carefully sampled and analyzed at equilibrium. In the present apparatus, VLE conditions are produced inside a thermo-regulated equilibrium cell (EC) (V = 34 cm3). The equilibrium cell consists of a sapphire tube (ST) held between two stainless steel flanges. Each flange contains valves and fittings for loading, discharging, degassing, and evacuation operations (LV1 and LV2), and provisions for temperature and pressure measurement. The equilibrium chamber contains an efficient stirring rod assembly (MS), driven by an external magnet attached to a stirring device (SD) (Heidolph, Germany, RZR 2020). The cell is placed in a thermo-regulated liquid bath (LB) and maintained at a desired operating temperature. Two 100 X platinum resistance thermometer probes (PP) (Actifa, France) are inserted into wells on the top and bottom stainless steel flanges. The VLE still is equipped with two pressure transducers (PT) (Druck, USA, PTX611): a high pressure

The two 100 X platinum resistance thermometer probes were calibrated against a 25 X platinum resistance thermometer (TINSLEY Precision Instruments, UK, Type 5187A). The 25 X reference probe was calibrated by the Laboratoire National d’Essais (Paris) based on the 1990 International Temperature Scale (ITS 90). The calibration data for the 100 X platinum resistance thermometer probes were fitted to second order polynomials by the method of least squares. The maximum correlation error for both temperature probes are estimated as ±0.02 K. The high pressure transducer was calibrated against a dead weight pressure balance (Desgranges and Hout, France, 5202S). The calibration data were fitted to a second order polynomial and the pressure correlation error is estimated as ±0.006 MPa. The response of the TCD was calibrated for each pure component via a syringe injection technique. Syringes (SGE, Australia) of volumes ranging from 100 to 500 lL were used for all components. The number of moles contained inside the syringes are estimated by using the ideal gas equation (n = PV/RT). The temperature and pressure of the gas inside the syringe are measured before each injection using a calibrated Pt-100 probe (Leris, France) with a correlation error of ±0.02 K, and a digital barometer (DRUCK, DPI141, with manufacturer stated uncertainty of ±1 Pa).

TABLE 1a Provenance and purity of materials studied. Compound

CAS registry no

Supplier

Volume fraction supplier

GC

Decafluorobutane C4F10 Propane C3H8 1-Butene C4H8

355-25-9 74-98-6 106-98-9

Pelchem (South Africa) Messer–Griesheim (France) Aldrich (Germany)

>0.995 >0.9995 >0.99

>0.995 >0.9995 >0.99

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PC

GC SD

TR

PT

SC

LS

VS

V5

V4 TR

VP

B2 LV2 PP

V1 V3

ST

VP V2

EC

LB

PT

MS TR

LV1 PP

B1 TP

EC

FIGURE 1. Flow diagram of the ‘‘static-analytic’’ apparatus. B1 and B2: product cylinders, EC: equilibrium cell, GC: gas chromatograph, LB: liquid bath, LS: liquid ROLSITM sampler, LV1 and LV2: loading valves, MS: magnetic stirrer, PC: personal computer, PP: platinum resistance thermometer probe, PT: pressure transducer, SC: ROLSITM sampler control, SD: stirring device, TP: thermal press, TR: temperature regulator, VP: vacuum pump, VS: vapour ROLSITM sampler, ST: sapphire tube, V1, V4: 3-way shut off valves, V2, V3, V5: 2-way shut off valves.

The syringe volume is read off the syringe thanks to a dedicated magnifying eye-piece. After multiple injections of various volumes of each pure component, a graph of detector response (peak area) versus number of moles is prepared. The calibration data for each pure component are fitted to second order polynomials and the maximum correlation errors on the mole numbers are estimated as ±1%, ±1.5%, and ±2% for propane, 1-butene, and decafluorobutane respectively. 2.4. Experimental procedure The equilibrium cell and all lines are evacuated using a vacuum pump (VP). The heavier component (decafluorobutane) is first introduced from cylinder (B2) via loading valve LV2, and the liquid bath thermostat is set to the desired temperature. The lighter component (propane or 1-butene) is charged to the cell through loading valve LV1, via a thermal press (TP), to a cell pressure corresponding to the desired pressure for the first measurement. The cell contents are stirred for approximately 30 min to accelerate the attainment of equilibrium and finally remove any concentration gradients. Phase equilibrium is assumed when the pressure transducers and temperature probes have stabilized to within their instrument uncertainty, for at least 10 min. The electromagnetic ROLSITM samplers are repeatedly purged or flushed with the equilibrium cell contents by sampling at larger opening times than for

the analyses. For each equilibrium condition, a minimum of five samples for both the vapour and liquid phases are withdrawn using the ROLSITM samplers. The resulting samples are analyzed to check for measurement repeatability. Average values are considered to correspond to the equilibrium value for each phase. Additional amounts of the lighter component (propane or 1-butene) are introduced to the equilibrium cell, and a new equilibrium condition established. This procedure is repeated until the entire composition range is covered for a desired isotherm. Thereafter, the equilibrium cell is evacuated and reloaded, and the procedure repeated for the next isothermal measurements. In some instances, the thermal press containing the lighter component is heated using a hotplate to facilitate charging from a higher pressure source. 2.5. Uncertainties Experimental uncertainties have been calculated taking into account the expanded uncertainties and coverage factor as described in Taylor and Kuyatt [30]. Combined standard uncertainties on temperature, pressure, and composition were calculated from the error associated with the calibration procedures (correlation errors and non-negligible errors), and from standard deviations estimated from repeated readings over the course of the measurements. A detailed description of the uncertainty calculations for the static analytic apparatus can be found in the thesis of Soo [31]. The

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2.6. Correlations

TABLE 1b Pure component parameters for decafluorobutane, propane, and 1-butene. Decafluorobutane

Propane

1-Butene

a

x

Critical properties and acentric factor 385.84 369.89 2.289 4.251 0.287 0.152

419.29 4.005 0.192

c1 c2 c3

Mathias–Copeman parametersb 0.938 0.630 0.751 0.454 3.064 1.974

0.670 0.159 0.512

Tc/K Pc/MPa

a Decafluorobutane parameters from DDB [33], propane and 1-butene parameters from REFPROP [32]. b 1-Butene parameters from Reid et al. [34], decafluorobutane and propane parameters determined in this work.

combined standard uncertainties are averaged over all data-sets and are reported as expanded uncertainties with a coverage factor of 2 at a confidence level of approximately 95%. The maximum expanded uncertainties on the experimental variables are estimated as (k = 2): U(T) = ±0.03 K, U(P) = ±0.007 MPa, U(x) = ±0.007 and U(y) = ±0.005 for the system (propane + decafluorobutane), and U(x) = ±0.006 and U(y) = ±0.005 for the system (1-butene + decafluorobutane).

The experimental VLE data are correlated with in-house thermodynamic software developed at the CEP/TEP laboratory. A symmetric (U–U) approach is used for the calculation of vapour and liquid phase fugacities via the cubic Peng–Robinson (PR) equation of state (EoS). The Mathias–Copeman (MC) expression is used as the alpha function in the attractive term of the EoS for a more accurate representation of vapour pressures. The critical properties and acentric factors for propane [32], 1-butene [32] and decafluorobutane [33] are reported in table 1b. The Mathias–Copeman parameters for propane and decafluorobutane were fitted to experimental vapour pressure data measured in this work, and parameters for 1butene were sourced from Reid et al. [34]. All MC parameters are reported in table 1b. The ‘‘PR–MC–WS–NRTL’’ model contains four interaction parameters adjustable to experimental data. The adjustable parameters are distributed among the mixing (a, s12, s21), and combining rules (k12). The non-randomness parameter a for the NRTL model is temperature independent, and was fixed at 0.3 in our data treatment. The system temperature and pressure are chosen as the independent variables and the following flash type objective function is used for the data treatment:

2 !2 3 2 X N  N X yexp  ycal xexp  xcal 4 5; F ¼ 100=N þ xexp yexp 1 1

ð1Þ

TABLE 2 Experimental and calculated propane vapour pressures. Texp/K

302.97 307.96 312.99 317.89 322.99 327.97 332.93 337.91 342.91

Pexp/MPa

1.072 1.214 1.361 1.522 1.712 1.906 2.103 2.336 2.582

REFPROP

PR–MC 2

Pcal/MPa

Pexp  Pcal/MPa

10 (Pexp  Pcal/Pexp)

Pcal/MPa

Pexp  Pcal/MPa

102(Pexp  Pcal/Pexp)

1.074 1.212 1.364 1.525 1.707 1.900 2.107 2.332 2.575

0.002 0.002 0.003 0.003 0.005 0.006 0.004 0.004 0.007

0.17 0.15 0.22 0.21 0.25 0.33 0.19 0.18 0.30 AARDP = 0.22%

1.073 1.211 1.364 1.525 1.708 1.901 2.110 2.336 2.580

0.001 0.003 0.003 0.003 0.004 0.005 0.007 0.000 0.002

0.05 0.23 0.18 0.20 0.22 0.25 0.31 0.01 0.08 AARDP = 0.17%

Expanded uncertainties (k = 2): U(T) = ±0.03 K, and U(P) = ±0.007 MPa.

TABLE 3 Experimental and calculated decafluorobutane vapour pressures. Texp/K

302.92 305.45 307.90 310.50 312.93 315.48 317.90 320.40 322.91 325.44 327.92 330.40 332.87 335.39 337.94 340.39 342.93

Pexp/MPa

0.316 0.339 0.366 0.393 0.419 0.455 0.487 0.522 0.560 0.595 0.633 0.675 0.718 0.762 0.819 0.860 0.919

REFPROP

PR–MC

Pcal/MPa

Pexp  Pcal/MPa

102(Pexp  Pcal/Pexp)

Pcal/MPa

Pexp  Pcal/MPa

102(Pexp  Pcal/Pexp)

0.312 0.337 0.363 0.392 0.421 0.452 0.484 0.519 0.555 0.594 0.634 0.676 0.720 0.767 0.816 0.866 0.920

0.004 0.002 0.003 0.001 0.002 0.003 0.003 0.003 0.005 0.001 0.001 0.001 0.002 0.003 0.003 0.006 0.001

1.40 0.50 0.81 0.29 0.35 0.47 0.58 0.68 0.83 0.13 0.19 0.18 0.18 0.56 0.36 0.67 0.19 AARDP = 0.49%

0.315 0.340 0.365 0.394 0.423 0.454 0.486 0.520 0.556 0.595 0.634 0.676 0.719 0.765 0.815 0.864 0.918

0.001 0.001 0.001 0.001 0.004 0.001 0.001 0.002 0.004 0.000 0.001 0.001 0.001 0.003 0.004 0.004 0.001

0.52 0.32 0.09 0.31 0.87 0.06 0.23 0.44 0.67 0.05 0.21 0.13 0.09 0.41 0.57 0.44 0.07 AARDP = 0.32%

Expanded uncertainties (k = 2): U(T) = ±0.03 K, and U(P) = ±0.007 MPa.

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TABLE 4 Experimental VLE pressures and experimental and calculated equilibrium phase compositions for the (propane + decafluorobutane) system. Pexp/MPa

x1exp

y1exp

x1cal

T/K = 312.92 0.726 0.814 0.909 0.964 1.005 1.123 1.207 1.255 1.306 1.344 1.369 1.372

0.134 0.184 0.250 0.296 0.329 0.445 0.551 0.628 0.721 0.820 0.910 0.965

0.093 0.161 0.200 0.227 0.300 0.337 0.461 0.570 0.653 0.752 0.893 0.931 0.961

0.432 0.504 0.567 0.598 0.623 0.692 0.738 0.769 0.815 0.861 0.923 0.964

0.134 0.186 0.250 0.292 0.328 0.444 0.552 0.628 0.725 0.821 0.916 0.965

0.053 0.111 0.191 0.332 0.462 0.533 0.610 0.702 0.772 0.871 0.932 0.960

y1exp  y1cal

Pexp/MPa

0.000 0.002 0.000 0.004 0.001 0.001 0.001 0.000 0.004 0.001 0.006 0.000

0.429 0.501 0.567 0.601 0.625 0.692 0.741 0.773 0.814 0.861 0.921 0.961

0.299 0.414 0.463 0.490 0.554 0.582 0.657 0.717 0.759 0.810 0.900 0.931 0.958

0.093 0.161 0.201 0.228 0.300 0.336 0.460 0.570 0.657 0.752 0.892 0.931 0.960

0.000 0.000 0.001 0.001 0.000 0.001 0.001 0.000 0.004 0.000 0.001 0.000 0.001

0.297 0.412 0.462 0.490 0.554 0.581 0.659 0.718 0.762 0.812 0.900 0.931 0.957

0.003 0.003 0.000 0.003 0.002 0.000 0.003 0.004 0.001 0.000 0.002 0.003

0.493 0.544 0.601 0.670 0.701 0.713 0.715 0.716 0.715 0.711 0.705 0.695 0.666 0.625

0.002 0.002 0.001 0.000 0.000 0.001 0.002 0.001 0.003 0.002 0.000 0.000 0.001

0.055 0.111 0.192 0.332 0.462 0.532 0.611 0.701 0.770 0.871 0.931 0.961

0.002 0.000 0.001 0.000 0.000 0.001 0.001 0.001 0.002 0.000 0.001 0.001

0.179 0.279 0.391 0.521 0.611 0.658 0.706 0.762 0.808 0.881 0.931 0.959

0.003 0.002 0.001 0.000 0.000 0.002 0.000 0.000 0.000 0.001 0.001 0.001

where N is the number of data points, xexp and xcal are the measured and calculated liquid compositions respectively, and yexp and ycal are the measured and calculated vapour compositions respectively. Statistical analyses are used to determine the quality of the fit of experimental data to the chosen thermodynamic model [35]. The definitions of the statistical estimators used herein for any property U are:

N 1X BiasU ð%Þ ¼ ðRDU ð%ÞÞ: N i¼1

1.163 1.357 1.411 1.463 1.472 1.479 1.475 1.460 1.431 1.344 1.307

0.058 0.107 0.180 0.310 0.410 0.521 0.561 0.581 0.641 0.740 0.821 0.870 0.920 0.952

0.073 0.110 0.171 0.344 0.511 0.540 0.581 0.590 0.671 0.730 0.810 0.883 0.922

0.131 0.290 0.362 0.471 0.513 0.570 0.652 0.720 0.810 0.904 0.921

x1exp  x1cal

y1cal

y1exp  y1cal

PR–MC–WS–NRTL 0.177 0.276 0.373 0.485 0.541 0.580 0.591 0.596 0.609 0.624 0.635 0.648 0.682 0.731

0.059 0.110 0.181 0.310 0.420 0.519 0.560 0.581 0.639 0.743 0.820 0.868 0.918 0.949

0.001 0.003 0.001 0.000 0.010 0.002 0.001 0.000 0.002 0.003 0.001 0.002 0.002 0.003

0.177 0.248 0.330 0.478 0.563 0.575 0.589 0.592 0.615 0.629 0.649 0.678 0.713

0.069 0.110 0.171 0.341 0.510 0.541 0.581 0.591 0.671 0.732 0.811 0.880 0.920

0.004 0.000 0.000 0.003 0.001 0.001 0.000 0.001 0.000 0.002 0.001 0.003 0.002

0.247 0.412 0.463 0.530 0.550 0.578 0.611 0.636 0.664 0.721 0.744

0.130 0.291 0.361 0.471 0.511 0.570 0.653 0.723 0.802 0.901 0.921

0.001 0.001 0.001 0.000 0.002 0.000 0.001 0.003 0.008 0.003 0.000

0.168 0.270 0.369 0.484 0.544 0.580 0.591 0.596 0.608 0.622 0.634 0.647 0.682 0.731

0.009 0.006 0.004 0.001 0.003 0.000 0.000 0.000 0.001 0.002 0.001 0.001 0.000 0.000

PR–MC–WS–NRTL 0.171 0.243 0.328 0.478 0.564 0.575 0.589 0.593 0.616 0.630 0.649 0.679 0.715

0.006 0.005 0.002 0.000 0.001 0.000 0.000 0.001 0.001 0.001 0.000 0.001 0.002

PR–MC–WS–NRTL 0.246 0.413 0.465 0.531 0.552 0.579 0.613 0.638 0.666 0.723 0.745

0.001 0.001 0.002 0.001 0.002 0.001 0.002 0.002 0.002 0.002 0.001

Expanded uncertainties (k = 2): U(T) = ±0.03 K, U(P) = ±0.007 MPa, U(x) ± 0.006, and U(y) ± 0.005.

TABLE 6 Parameters for the PR–MC–WS–NRTL model fitted to experimental VLE data for the (propane + decafluorobutane) and (1-butene + decafluorobutane) systems. T/K

s12

312.92 327.94 342.94

Propane + decafluorobutanea 1662 2235 2296 1970 2734 1795

0.297 0.269 0.251

312.92 327.93 342.93

1-Butene + decafluorobutaneb 8009 1252 8213 1430 8341 1477

0.251 0.232 0.227

ð2Þ

Using the above definition, the absolute average deviation (AARD) and bias are defined as: N 1X AARDU ð%Þ ¼ jRDU ð%Þj; N i¼1

x1cal

T/K = 342.93

Expanded uncertainties (k = 2): U(T) = ±0.03 K, U(P) = ±0.007 MPa, U(x) ± 0.007, and U(y) ± 0.005.

  U exp  U col : RDU ð%Þ ¼ 100 U exp

y1exp

T/K = 327.93 0.744 0.798 0.867 0.992 1.042 1.045 1.047 1.047 1.043 1.037 1.021 0.990 0.948

PR–MC–WS–NRTL 0.182 0.281 0.392 0.521 0.611 0.656 0.706 0.762 0.808 0.880 0.930 0.958

x1exp

T/K = 312.92

PR–MC–WS–NRTL

T/K = 342.94 1.135 1.298 1.526 1.856 2.109 2.229 2.351 2.465 2.535 2.597 2.605 2.601

y1cal

PR–MC–WS–NRTL

T/K = 327.94 0.908 1.072 1.157 1.209 1.339 1.397 1.571 1.697 1.778 1.849 1.910 1.916 1.914

x1exp  x1cal

TABLE 5 Experimental VLE pressures and experimental and calculated equilibrium phase compositions for the (1-butene + decafluorobutane) system.

a b

s21

k12

k12 = 0.001T/K + 0.773, s12 = 35.71T/K  9482, s21 = 14.63I/K + 6798. k12 = 0.0007T/K + 0.488, s12 = 11.07IT/K + 4557, s21 = 7.481T/K  1066.

ð3Þ

ð4Þ

High AARDU values are indicative of either a systematic or large random difference between the experimental data and the correlating model. The biasU value is the average deviation of the data

set, and large positive or negative values indicate systematic differences between the data and the chosen model. Experimental data sets are accurately represented by a correlating model when these statistical parameters are near zero. The location of the azeotrope was calculated by the method described in Coquelet et al. [36]. An azeotrope corresponds to an extremum of temperature or pressure. At this point, the

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139

ð@P=@xi ÞT ¼ 0 for N  1:

ð6Þ

yi ¼ xi

ð7Þ

for i ¼ 1 to N;

where N is the number of components in the mixture. At the azeotropic point, the mixture is treated as a pure component and the EoS mixture attractive parameter (a) is the same in both the liquid and vapour phases (al = av). The location of the azeotrope is calculated by determining the equilibrium composition that satisfies this equality via a simple secant method [36]. Relative volatility (aij) values were estimated from the experimental and calculated mixture data. 3. Results and discussion

FIGURE 2. Experimental VLE data and modelling results for the system (propane + decafluorobutane) at various temperatures: 312.92 K (s); 327.94 K (d); 342.94 K (4); PR–MC–WS–NRTL model (—); Calculated azeotropic line (h).

FIGURE 3. Experimental VLE data and modelling results for the system (1butene + decafluorobutane) at various temperatures: 312.92 K (s); 327.93 K (d); 342.93 K (4); PR–MC–WS–NRTL model (—); Calculated azeotropic line (h).

TABLE 7 Calculated azeotropic pressures and compositions for the two binary systems studied. T/K

P/MPa

x1

312.92 327.94 342.94

Propane + decafluorobutane 1.371 1.921 2.613

0.946 0.934 0.924

312.92 327.93 342.93

1-Butene + decafluorobutane 0.721 1.053 1.482

0.601 0.593 0.587

compositions of both the liquid and vapour phases are equal, and the system can be expressed by the following set of conditions:

ð@T=@xi ÞP ¼ 0 for N  1;

ð5Þ

Experimental saturated vapour pressures of propane and of decafluorobutane are reported in tables 2 and 3. The measured vapour pressure data cover the temperature range of the VLE measurements and were used to fit MC parameters for the PR EoS, table 1b. The deviations in pressure for the regression of the alpha function parameters are reported in tables 2 and 3. In general, the PR EoS with the implemented MC expression provides a good correlation of the vapour pressure data with absolute average deviations on pressure (AARDP) of 0.17% and 0.32% for propane and decafluorobutane respectively. The experimental data were also compared to values calculated from high accuracy reference EoS for propane [37] and decafluorobutane [38] from REFPROP [32]. The pressure deviations for these comparisons are reported in tables 2 and 3. The experimental data are found to be consistent with the literature correlations with AARDP of 0.22% and 0.5% for propane and decafluorobutane respectively. Experimental (P–x–y) VLE data for the (propane + decafluorobutane), and (1-butene + decafluorobutane) binary systems are reported in tables 4 and 5. The VLE data for both systems were measured at three temperatures below the critical temperatures of all components. The binary mixture data were used to fit interaction parameters for the ‘‘PR–MC–WS–NRTL’’ model, see table 6. Parameters were fitted to individual isotherms for each system and exhibit linear temperature dependence; linear expressions are reported at the bottom of table 6. The experimental VLE data and their representation through the ‘‘PR–MC–WS–NRTL’’ model are plotted in figure 2 for the system (propane + decafluorobutane), and in figure 3 for the system (1-butene + decafluorobutane). Azeotropic behaviour was observed for both systems at all investigated temperatures. For the system (propane + decafluorobutane), maximum pressure azeotropy was observed at high propane concentrations. This is characteristic of systems where azeotrope formation is strongly influenced by molecular interactions rather than a similarity of pure component vapour pressures. Moreover, for systems with positive deviations from ideality, attractive intermolecular forces between molecules of the same species are usually stronger than interactions between different species [39], which could possibly account for the azeotrope formation at propane mole fractions > 0.92. For (1-butene + decafluorobutane) binary mixtures, maximum pressure azeotropy was also observed, but at intermediate 1-butene concentrations. Such behaviour is characteristic of systems where the pure component vapour pressure ratio is close to unity. The limiting case is the situation where the saturated vapour pressures of the two components are equal at some temperature, termed the Bancroft point [40]. Extrapolation of the pure component vapour pressures for 1-butene and decafluorobutane reveals the occurrence of a Bancroft point at T = 373.43 K (1.796 MPa). For systems that exhibit a Bancroft point, the composition dependence of the azeotrope (for increasing temperature) is typically towards the component whose vapour pressure changes more rapidly with temperature [39–41],

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FIGURE 4. Deviation of experimental liquid and vapour compositions for the system (propane + decafluorobutane) from values calculated via the ‘‘PR–MC–WS–NRTL’’ model at various temperatures: 312.92 K (s); 327.94 K (d); 342.94 K (4).

FIGURE 5. Deviation of experimental liquid and vapour compositions for the system (1-butene + decafluorobutane) from values calculated via the ‘‘PR–MC–WS–NRTL’’ model at various temperatures: 312.92 K (s); 327.93 K (d); 342.93 K (4).

in this system decafluorobutane. The calculated [36] azeotropic pressures and compositions are reported in table 7 for both systems, and are plotted with the VLE data in figures 2 and 3. The systems studied do not exhibit liquid–liquid immiscibility over the

range of temperatures investigated in this work. However, Gilmour et al. [15] have reported (liquid + liquid) equilibrium data for the system (propane + decafluorobutane) at lower temperatures (204 K). Deviations between the experimental and calculated

S.C. Subramoney et al. / J. Chem. Thermodynamics 67 (2013) 134–142 TABLE 8 Absolute average deviation (AARD) and bias values for the fitting of experimental VLE data to the ‘‘PR–MC–WS–NRTL’’ model for the two binary systems studied. T/K

AARDx1/%

AARDy1/%

Biasx1/%

312.92 327.94 342.94

0.33 0.21 0.49

Propane + decafluorobutane 0.29 0.05 0.20 0.03 0.25 0.27

312.92 327.93 342.93

0.62 0.58 0.29

1-Butene + decafluorobutane 0.74 0.36 0.55 0.50 0.28 0.16

Biasy1/% 0.02 0.04 0.19 0.66 0.39 0.17

141

for (1-butene + decafluorobutane). In addition, the AARD and bias on equilibrium compositions for the fitting of the experimental results are listed in table 8 for both systems. In general, the experimental VLE data were well correlated by ‘‘PR–MC–WS–NRTL’’ model over the entire composition range at all temperatures for both systems (AARDx1,y1 < 1%). An accurate description of the relative volatility (aij) of mixtures is essential for good process design. Relative volatilities were calculated from the experimental data and compared to values calculated from the ‘‘PR–MC–WS–NRTL’’ model. The composition dependence of aij is plotted in figure 6 for (propane + decafluorobutane), and in figure 7 for (1-butene + decafluorobutane). A line of constant relative volatility (a12 = 1) is indicated on the figures to show the location of the azeotrope. In general, a good agreement between the experimental and calculated relative volatility values was observed over the entire composition range for all temperatures studied. 4. Conclusions

FIGURE 6. Composition dependence of relative volatility (a12) for the system (propane + decafluorobutane) at various temperatures: 312.92 K (s); 327.94 K (d); 342.94 K (4); Line of constant relative volatility a12 = 1 (); PR–MC–WS–NRTL model (—). Error bands: ±6% for experimental results.

Novel isothermal (P–x–y) VLE data are presented at three temperatures each for the (propane + decafluorobutane), and (1-butene + decafluorobutane) binary systems over the 312.92 K to 342.94 K temperature range. The experimental values were measured on a ‘‘static-analytic’’ type apparatus taking advantage of two electromagnetic ROLSITM capillary samplers for repeatable and reliable equilibrium phase sampling and handling. The experimental results are given with the following expanded uncertainties (k = 2): U(T) = ±0.03 K, U(P) = ±0.007 MPa, U(x) = ±0.007 and U(y) = ±0.005 for the system (propane + decafluorobutane), and U(x) = ±0.006 and U(y) = ±0.005 for the system (1-butene + decafluorobutane). The VLE results were well correlated with in-house thermodynamic software based on the ‘‘PR–MC–WS–NRTL’’ model. Maximum pressure azeotropy was observed at all temperatures studied for both systems. Liquid–liquid immiscibility is not observed for either system over the range of temperatures investigated from 312.92 K to 342.94 K. Acknowledgements This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology, and National Research Foundation. Pelchem is acknowledged for the supply of decafluorobutane (R-610). References

FIGURE 7. Composition dependence of relative volatility (a12) for the system (1butene + decafluorobutane) at various temperatures: 312.92 K (s); 327.93 K (d); 342.93 K (D); Line of constant relative volatility a12 = 1 (); PR–MC–WS–NRTL model (—). Error bands: ±7% for experimental results.

(‘‘PR–MC–WS–NRTL’’) liquid and vapour compositions are reported with the VLE data in tables 4 and 5, and scatter diagrams plotted in figure 4 for the system (propane + decafluorobutane), and figure 5

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JCT 13-279